BT_devTweedie {BT} | R Documentation |

## Deviance function for the Tweedie family.

### Description

Compute the deviance for the Tweedie family case.

### Usage

```
BT_devTweedie(y, mu, tweedieVal, w = NULL)
```

### Arguments

`y` |
a vector containing the observed values. |

`mu` |
a vector containing the fitted values. |

`tweedieVal` |
a numeric representing the Tweedie Power. It has to be a positive number outside of the interval ]0,1[. |

`w` |
an optional vector of weights. |

### Details

This function computes the Tweedie related deviance. The latter is defined as:

`d(y, mu, w) = w (y-mu)^2, if tweedieVal = 0;`

`d(y, mu, w) = 2 w (y log(y/mu) + mu - y), if tweedieVal = 1;`

`d(y, mu, w) = 2 w (log(mu/y) + y/mu - 1), if tweedieVal = 2;`

`d(y, mu, w) = 2 w (max(y,0)^(2-p)/((1-p)(2-p)) - y mu^(1-p)/(1-p) + mu^(2-p)/(2-p)), else.`

### Value

A vector of individual deviance contribution.

### Author(s)

Gireg Willame gireg.willame@gmail.com

*This package is inspired by the gbm3 package. For more details, see https://github.com/gbm-developers/gbm3/*.

### References

M. Denuit, D. Hainaut and J. Trufin (2019). **Effective Statistical Learning Methods for Actuaries |: GLMs and Extensions**, *Springer Actuarial*.

M. Denuit, D. Hainaut and J. Trufin (2019). **Effective Statistical Learning Methods for Actuaries ||: Tree-Based Methods and Extensions**, *Springer Actuarial*.

M. Denuit, D. Hainaut and J. Trufin (2019). **Effective Statistical Learning Methods for Actuaries |||: Neural Networks and Extensions**, *Springer Actuarial*.

M. Denuit, D. Hainaut and J. Trufin (2022). **Response versus gradient boosting trees, GLMs and neural networks under Tweedie loss and log-link**.
Accepted for publication in *Scandinavian Actuarial Journal*.

M. Denuit, J. Huyghe and J. Trufin (2022). **Boosting cost-complexity pruned trees on Tweedie responses: The ABT machine for insurance ratemaking**.
Paper submitted for publication.

M. Denuit, J. Trufin and T. Verdebout (2022). **Boosting on the responses with Tweedie loss functions**. Paper submitted for publication.

### See Also

*BT*version 0.4 Index]